Blender cycles glow on transparent background
You should do this kind of things in the compositor node.
Replace the background plane's material with a holdout node.

Then, setup your compositing like this:



You can animate the size value to change the amount of glow in the rendering. Keep in mind that you will need to adjust the size of you image to not cut of the glow at the edges. Also try out different blur algorithms, the Gaussian doesn't work that well in this use case (personally, I liked Quadratic)

EDIT

If you want to hat the blur another color, put in the Alpha pass instead of the Image pass into the Blur node. Using a color node in between, you can have the glare every color: 



EDIT 2

Sorry, I forgot the transparent background:



The input for the alpha needs to be a white blurred image, so iIf you are using a colored glare, put the color node behind the blue or duplicate the blur node and keep both synchronized. The max node is needed to make sure that the sign will always be fully opaque since the blurring is done into both directions: outside and inside of the image.

EDIT 3

If you want to restrict the effect to specific areas, create a black/white mask and color multiply if with the output of the blur node. In your case, the inside/outside is defined by the alpha pass of the rendering.



Now, the center of your image will be without glow effect. To have actual transparency in the image, you probably will need to add another mask to the alpha output but that shouldn't be a problem anymore.